1/3k+1/2k=10

Solution for 1/3k+1/2k=10 equation:

1/3k+1/2k=10

We move all terms to the left:

1/3k+1/2k-(10)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We calculate fractions


2k/6k^2+3k/6k^2-10=0

We multiply all the terms by the denominator


2k+3k-10*6k^2=0

We add all the numbers together, and all the variables

5k-10*6k^2=0

Wy multiply elements

-60k^2+5k=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$